Create (Unwrap) a UV Map after Adding Texture to the Image Editor
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A wild guess... if you've rescaled your object at any point you need to apply this change. Select the object you're unwrapping, Tab to Object mode, tap Ctrl  + A and choose Scale. Then try the unwrap again and see if this fixes your issue. 

Edit: This appears to be a difference in the way UVs are unwrapped between the Internal renderer and the Cycles renderer. Switching to cycles and unwrapping gives the desired result.